{ comments are enclosed by curly-braces;
  no nested comments are allowed  }

{ addition 

  these rules work when the arguments are numerals
  but not for all arbitrary expressions

}



Add Z y => y;
Add (S x) y => S (Add x y);

Add (Add x y) z => Add x (Add y z);
Add (Mult (S x) y) z => Add y (Add (Mult x y) z);
Add (Mult Z y) z => z;

{ define multiplication (Mult) here }

Mult (Add x y) z => Add (Mult x z) (Mult y z) ;

Mult Z y => Z;
Mult (S x) y => Add y (Mult x y);

Mult (Mult x y) z => Mult x (Mult y z) ;




{ when all other computation is done } 
Compute x => x;

. { end of rules }